The present invention relates to signal coding.
During the past decade, coded modulation has proven to be a practical, power-efficient and bandwidth-efficient modulation technique for channels with additive white Gaussian noise (AWGN). Such techniques have now been widely used in commercial telephone voiceband modems and have resulted in an increase in the commercially achievable line rates of those modems up to 19.2K bits/s.
Coded modulation techniques are often used in conjunction with 2N-dimensional signal constellations, N.gtoreq.1. For cases of N&gt;1, in particular, a 2N-dimensional signal constellation can be formed by concatenating N/M constituent 2M-dimensional constellations. Usually, M=1 so that N constituent two-dimensional (2 D) constellations are used. The concatenation of the constituent 2 D constellations is usually performed in the time domain, although it can also be done in the frequency, polarization or space domains or combinations thereof.
Within the context of coded modulation techniques, an engineering tradeoff is required in terms of the dimensionality of the constellation used. On the one hand, using higher-dimensional constellations reduces the required size of the constituent 2 D constellations. This is advantageous in that the signalling will be more robust in the presence of impairments other than AWGN, such as non-linear distortions, residual intersymbol interference and phase jitter, as is the case in telephone voiceband modems. Disadvantageously, on the other hand, the decoding delay in the receiver increases almost linearly with 2N, i.e., with the dimensionality of the constellation.
The issues may be even more complex. For example, making maximum use of the available bandwidth in a bandwidth-limited environment, such as telephone voiceband transmission, may dictate use of a particular baud rate. For example, in telephone voiceband applications a baud rate of 2,742.86 (=19,200.div.7) is typical. At the same time, however, most present-day data transmission is carried out at a selected one of a limited set of standard bit rates, e.g., 14.4K bits/s. Given a particular dimensionality, say, 2N, of the selected constellation, the selected baud and bit rates may result in a fractional number of information bits per 2N-dimensional symbol (hereinafter "fractional bit rate"). For example, use of a 2 D constellation with the above baud and bit rates results in a fractional bit rate of 14,400/2,742.86=5.25 bits per 2 D symbol. Even when the rate desired to be used in a given application does not result in a fractional bit rate, such may result when, for example, a fallback bit rate is used in conjunction with the selected baud rate. A fallback bit rate is desirable for continuous operation of transmission equipment when the channel condition deteriorates.
To this point, the prior art has favored the use of a constellation of sufficient dimensionality that a fractional bit rate does not occur. Thus, in the example above, the fractional bit rate of 5.25 occurring with a 2 D constellation is avoided by using a 8D constellation with a bit rate of 21 bits per 8 D symbol. The reason for this is that achieving a fractional bit rate with, say, a 2 D constellation may necessitate the use of two or more different size 2 D constellations, one of which will, disadvantageously, always be larger than the constituent 2 D constellations of a higher-dimensional scheme at the same bit rate. Thus, continuing with the above example, a fractional bit rate of 5.25 would be achieved in a conventional 2 D trellis coding scheme--which adds a single redundant bit per 2 D symbol--by transmitting 6, 6, 6 and 7 bits periodically in successive four symbol intervals using 2.sup.6 =64- and 2.sup.7 =128-symbol constellations. The average bit rate, then, is, of course, the average of 6, 6, 6 and 7, or 6.25, as desired. Alternatively, an 8 D trellis coding scheme can be used in which 4.times.5.25=21 data bits are communicated for each 8 D symbol along with a single redundant bit to provide an encoded bit rate of 22 bits per 8 D symbol. The 8 D constellation would then have 2.sup.22 8 D symbols, which can be represented by concatenating a sequence of four 48-signal-point constituent 2 D constellations. Thus the 8D scheme, because it uses the 48-point 2 D constellation exclusively--as contrasted to the combination of 64-symbol and 128-symbol constellations--provides somewhat better performance, for the reasons discussed hereinabove. Disadvantageously, however, the decoding delay for the 8 D trellis code may be significantly greater than that of the first-mentioned, 2 D trellis-encoding scheme.